Riding mowers and other vehicles that traverse moderately rough terrain have long been known for transmitting vibrations to the operator. This problem is particularly acute for riding mowers. Because riding mowers must follow terrain variations in order to properly cut turf and because the cutting decks of riding mowers are typically carried by the frame of a riding mower. Because of this, when riding mowers do have suspension systems between the wheels and the frame, the range of relative motion between the wheels and the frame are usually limited so that the quality of the cut is not compromised. Accordingly, various suspension systems have been interposed between mower frames and operator seats or operator platforms in order to isolate operators from terrain variations. All suspension systems rely on the fundamental property of inertia. Accordingly, if the operator and the operator's seat can be at least partially decoupled from the vehicle frame, then the operator and the operator's seat would generally continue their motion and direction of motion regardless of sudden variations in the path of the mower. Further, since the direction of motion of a riding mower is generally in the longitudinal or “x” direction, the path variations which are most likely to cause discomfort for an operator are in the vertical or “y” direction as well as, and nearly as importantly, in the longitudinal or “x” direction. The ability to absorb displacements in the longitudinal or “x” direction is particularly important for riding mowers having relatively short wheel bases. When such “short coupled” riding mowers encounter a bump, the mower will suddenly rotate about a generally transverse axis causing “back slap” (when the back of the operator seat to slaps the operators back). If the operator's seat can translate in the longitudinal direction, then back slap can be reduced. Yet, most prior art riding mower suspension systems employ a spring element which compresses only in response to vertical forces. Also, suspension systems having compression springs or elastomeric compression elements usually have a limited range of motion. Accordingly, what is needed is an operator seat suspension system that is compliant in the vertical or “y” direction, as well as being compliant in the longitudinal or “x” direction and with a generous range of motion in both the “x” and “y” directions. Further, it would be advantageous if such a suspension system had a means for dampening responsive relative motions between the operator seat and the vehicle frame in the vertical or “y” direction and in the longitudinal or “x” direction.